Building Design and Construction Handbook - Merritt - Ventech!

COLD-FORMED STEEL CONSTRUCTION 8.17
8.6 UNSTIFFENED COLD-FORMED ELEMENTS
SUBJECT TO LOCAL BUCKLING
As indicated in Art. 8.5, the effective width of an unstiffened element in compression
may be computed from Eqs. (8.5) to (8.7). By definition, unstiffened elements
have only one edge in the direction of compression stress supported by a web or
stiffened element while the other edge has no auxiliary support (Fig. 8.6a). The
coefficient k in Eq. (8.5) is 0.43 for such an element. When the flat-width-to-
thickness ratio does not exceed 72/ �ƒ,
where ƒ � compressive stress, ksi, an
unstiffened element is fully effective and b � w. Generally, however, Eq. (8.5)
becomes
1.052(w/t)�ƒ/E
� � � 0.0093(w/t)�ƒ (8.8)
�0.43
where E � 29,500 ksi for steel. Substitution of � in Eq. (8.7) yields b/w � �. Fig.
(8.7a) shows a nest of curves for the relationship of b/t to w/t for unstiffened
elements for w/t between 0 and 60 with ƒ between 15 and 90 ksi.
In beam deflection determinations requiring use of the moment of inertia of the
cross section, the allowable stress ƒ is used to calculate the effective width of an
unstiffened element in a cold-formed steel member loaded as a beam. However, in
beam strength determinations requiring use of the section modulus of the cross
section, 1.67ƒ is the stress to be used in Eq. (8.8) to calculate the effective width
of the unstiffened element and provide an adequate margin of safety.
In determination of safe loads for a cold-formed steel section used as a column,
the effective width for an unstiffened element should be determined for a nominal
buckling stress, F n, to ensure an adequate margin of safety.
8.7 STIFFENED COLD-FORMED ELEMENTS
SUBJECT TO LOCAL BUCKLING
As indicted in 8.5, the effective width of a stiffened element in compression may
be computed from Eqs. (8.5) to (8.7). By definition, stiffened elements have one
edge in the direction of compression stress supported by a web or stiffened element
and the other edge also supported by a qualified stiffener (Fig. 8.6b). The coefficient
k in Eq. (8.5) is 4.00 for such an element. When the flat-width-to-thickness ratio
does not exceed 220/ �ƒ,
where ƒ � compressive stress, ksi, computed on the basis
of the effective section, a stiffened element is fully effective and b � w. Generally,
however, Eq. (8.5) becomes
1.052(w/t)�ƒ/E
� � � 0.0031(w/t)�ƒ (8.9)
�4
where E � 29,500 ksi for steel. Substitution of � in Eq. (8.7) yields b/w � �.
Moreover, when � � 0.673, b � w and when � � 0.673, b � �w. Figure 8.7b
shows a nest of curves for the relationship of b/t to w/t for stiffened elements for
w/t between 0 and 500 with ƒ between 10 and 90 ksi.
In beam deflection determinations requiring use of the moment of inertia of the
cross section, the allowable stress ƒ is used to calculate the effective width of a